A thin disc of mass M and radius R rotates in a horizontal plane about its central perpendicular axis at ω. Another disc of the same dimensions but mass M/2 is placed gently and co-axially on it. The new common angular velocity is

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(2) 2/3ω. Conserve angular momentum: I₁ω=(I₁+I₂)ω' with I₁=1/2 MR², I₂=1/2·/M2 R²=1/4 MR². ω'=(I₁)/(I₁+I₂)ω=(1/2)/(1/2+1/4)ω=2/3ω.

A thin disc of mass M and radius R rotates in a horizontal plane about its central perpendicular axis at ω. Another disc of the same dimensions but mass M/2 is placed gently and co-axially on it. The new common angular velocity is

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